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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Second order parabolic equations in Banach spaces with dynamic boundary conditions


Authors: Ti-Jun Xiao and Jin Liang
Journal: Trans. Amer. Math. Soc. 356 (2004), 4787-4809
MSC (2000): Primary 34G10, 47D06, 35G10
Published electronically: June 25, 2004
MathSciNet review: 2084398
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Abstract: In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.


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Additional Information

Ti-Jun Xiao
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany
Email: xiaotj@ustc.edu.cn, tixi@fa.uni-tuebingen.de

Jin Liang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany
Email: jliang@ustc.edu.cn, jili@fa.uni-tuebingen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03704-3
PII: S 0002-9947(04)03704-3
Keywords: Differential equations in Banach spaces, second order (in time), parabolic type, dynamic boundary conditions, strict and classical solutions
Received by editor(s): June 24, 2002
Published electronically: June 25, 2004
Additional Notes: The first author acknowledges support from the Alexander-von-Humboldt Foundation and from CAS and NSFC. The second author acknowledges support from the Max-Planck Society and from CAS and EMC
Article copyright: © Copyright 2004 American Mathematical Society